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On the roots of certain Dickson polynomials.
- Source :
-
Journal of Number Theory . Jul2018, Vol. 188, p229-246. 18p. - Publication Year :
- 2018
-
Abstract
- Let n be a positive integer, q = 2 n , and let F q be the finite field with q elements. For each positive integer m , let D m ( X ) be the Dickson polynomial of the first kind of degree m with parameter 1. Assume that m > 1 is a divisor of q + 1 . We study the existence of α ∈ F q ⁎ such that D m ( α ) = D m ( α − 1 ) = 0 . We also explore the connections of this question to an open question by Wiedemann and a game called “Button Madness”. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 188
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 128651090
- Full Text :
- https://doi.org/10.1016/j.jnt.2018.01.003